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Aflati cel mai mic numar natural care impartit pe rand la numere 24, 36 si 40 da resturile : 17, 29 si 33

Răspuns :

Hatty
a: 24=c1 rest 17
a: 36=c2 rest 29
a: 40=c3 rest 33
=>a=24*c1+17
a=36*c2+29
a=40*c3+33
Adunam 7
.............,...................
a+7=24*c1+24
a+7=36*c2+36
a+7=40*c3+40
a+7=24(c1+1)
a+7=36(c2+1)
a+7=40(c3+1)
=>a+7€M[24,36, 40]
=>a+7€M[360]={0, 360,720,1080.....}
=>a+7=360
a=353
Didi12342
a : 24 = x rest 17 ==> a = 24x+17 |+7
a : 36 = y rest 29 ==> a = 36y+29 |+7
a : 40 = z rest 33 ==> a = 40z+33 |+7

==> a + 7 = 24(x+1)
==> a + 7 = 36(y+1)
==> a+7 = 40(z+1)

24 = 2^3 × 3
36 = 2^2 × 3^2
40 = 2^3 × 5
--------------------
c.m.m.m.c = 2^3 × 3^2 × 5 = 360

a + 7 = 360
a= 360-7
a = 353 (numarul cautat)

Verificare:
353 : 24 = 14 rest 17
353 : 36 = 9 rest 29
353 : 40 = 8 rest 33

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